The paper is devoted to problem of analysis, identification and prediction of the presence of damages, which above a certain level may present a serious threat to the engineering (vibrating) structures such as different technical systems (hydrotechnical equipment, hydroelectrical station engines, atomic reactors ones etc). Usually change of structural dynamic properties due to environmental, operational and other effects allows to determine the existence, location and size of damages. We present and apply an effective computational approach to modelling, analysis of chaotic behaviour of structural dynamic properties of the engineering structures. The approach includes a combined group of non-linear analysis and chaos theory methods such as a correlation integral approach, average mutual information, surrogate data, false nearest neighbours algorithms, the Lyapunov’s exponents and Kolmogorov entropy analysis, nonlinear prediction models etc. As illustration we present the results of the numerical investigation of a chaotic elements in dynamical parameter time series for the experimental cantilever beam (environmental conditions are imitated by damaged structure, variating temperature, availability of a pinknoise force). For the first time we list the numerical data on topological and dynamical invariants, i.e., correlation, embedding, Kaplan-Yorke dimensions, Lyapunov’s exponents and Kolmogorov entropy etc.
[1] Hoon S.: Philos. Trans. R. Soc. A, 2007, 365, 539
[2] Limongelli M.:Mech. Syst. Signal Process., 2010, 24, 2898
[3] Tjirkallis A. and Kyprianou A.: Mech. Syst. Signal Process., 2016, 66–67, 282
[4] Glushkov A. V., Khokhlov V. N., Serbov N. G., Buyadzhi V. V., Bunyakova Yu. Ya., Solyanikova E. P.: Environmental Problems., 2016, 1(2), 111.
[5] Glushkov A. V., Safranov T. A., Khetselius O. Yu., Ignatenko A. V., Buyadzhi V. V., Svinarenko A. A.: Environmental Problems., 2016, 1(2), 115
[6] Glushkov A. V., Safranov T. A., Khetselius O. Yu., Prepelitsa G. P., Mansarliysky V. F., Bykowszczenko N.: Environmental Problems., 2016, 1(2), 105
[7] Alsberg В. К., Woodward A. M., Winson M. K., Rowland J. J. and Kell D. B.: Analytica Chim. Acta., 1988, 368, 29.
[8] Jubran B. A., Hamdan M. N., Shabaneh N. H.: Int. J. Eng. Science. 1998, 36, 843.
[9] Kofidis E., Kolokotronis N., Vassilarakou A., Theodoridis S., Cavouras D.: Future Generation Comp. Syst., 1999, 15, 223.
[10] Lin W-H., Lee J-S., Chen C-H., Sun Y-N.: Signal Proc. 1998, 65, 103.
[11] Liu G. R., Han X., Lam K. Y.: Composites Part B: Engineering., 1999, 30, 383
[12] Bunyakova Yu. Ya., Glushkov A. V.: Analysis and forecast of the impact of anthropogenic factors on air basein of an industrial city. Odessa, Ecology, 2010.
[13] Glushkov A. V., Bunyakova Yu. Ya., Buyadzhi V. V., Dubrovskaya Yu. V., Kuznetsova A. A., Khetselius O. Yu.: Sensor Electr. and Microsystem Techn., 2017, 14(3), 24.
[14] Glushkov A. V.: Methods of a chaos theory. Odessa, Astroprint, 2012.
[15] Glushkov A. V.: Relativistic Quantum Theory. Quantum, mechanics of Atomic Systems. Odessa, Astroprint, 2008.
[16] Packard N. H., Crutchfield J. P., Farmer J. D., Shaw R.: Phys. Rev. Lett., 1980, 45, 712.
[17] Gallager R. G.: Information theory and reliable communication, N-Y., Wiley, 1986.
[18] Abarbanel H. D. I., Brown R., Sidorowich J. J., Tsimring L. Sh.: Rev. Mod. Phys., 1993, 65, 1331
[19] Schreiber T.: Phys. Rep., 1999, 1, 308.
[20] Grassberger P., Procaccia I.: Physica D., 1983, 9, 189.
[21] Kennel M. B., Brown R. and Abarbanel H. D. I.: Phys. Rev. A., 1992, 45, 3403.
[22] Khokhlov V. N., Glushkov A. V., Tsenenko I. A.: Nonlinear Processes in Geophysics., 2004, 11, 295.
[23] Glushkov A. V., Khokhlov V. N., Prepelitsa G. P., Tsenenko I. A.: Optics of atm. and ocean, 2004, 14, 219.
[24] Glushkov A. V., Khetselius O. Yu., Kuzakon V. M., Prepelitsa G. P., Solyanikova E. P., Svinarenko A. A.: Dynamical Systems – Theory and Applications, 2011, BIF110.
[25] Glushkov A. V., Kuzakon V. M., Khetselius O. Yu. etal: Proc. of Internat. Geometry Center, 2013, 6, No. 6.
[26] Bunyakova Yu. Ya., Khetselius O. Yu.: Proc. of 8th Int. Carbon Dioxide Conference (Germany), 2009, T2-098.
[27] Glushkov A. V., Kuzakon V. M., Khetselius O. Yu., TernovskyV. B.: Proc. Int. Geom. Centre., 2015, 8(3-4), 91.
[28] Glushkov A. V., Khetselius O. Y., Brusentseva S. V., Zaichko P. A., Ternovsky V. B.: Advances in Neural Networks, Fuzzy Systems and Artificial Intelligence. Series: Recent Advances in Computer Engineering (Gdansk), 2014, 21, 69.
[29] Glushkov A. V., Svinarenko A. A., Buyadzhi V. V., Zaichko P. A., Ternovsky V. B.: Advances in Neural Networks, Fuzzy Systems and Artificial Intelligence, Series: Recent Advances in Computer Engineering (Gdansk), 2014, 21, 143.
[30] Glushkov A., Vaschenko V., Gerasimenko G., Bunyakova Yu.: Dynamical Systems Applications, Eds. J. Awrejcewicz, M. Kazmierczak, P. Olejnik, J. Mrozowski (Lodz, Polland), 2013, T2, 241.
[31] Khetselius O. Yu.: Dynamical Systems Applications, Eds. J. Awrejcewicz, M. Kazmierczak, P. Olejnik, J. Mrozowski (Lodz, Polland), 2013, T2, 145.
[32] Glushkov A. V., Kuzakon V. M., Ternovsky V. B., Buyadzhi V. V.: Dynamical Systems Theory Eds. J. Awrejcewicz, M. Kazmierczak, P. Olejnik, J. Mrozowski (Lodz), 2013, 1, 461.
[33] Glushkov A. V., Khetselius O. Yu., Gurnitskaya E. P. Loboda A. V., Florko T. A., Sukharev D. E., Lovett L.: Frontiers in quantum systems in chemistry and physics (Springer), 2008, 18, 507.
[34] Glushkov A. V., Svinarenko A. A., Khetselius O. Yu., Buyadzhi V. V., Florko T. A., Shakhman A. N., Frontiers in Quantum Methods and Applications in Chemistry and Physics (Springer, Cham), 2015, 29, 197.
[35] Buyadzhi V. V., Glushkov A. V., Mansarliysky V. F., Ignatenko A. V., Svinarenko A. A.: Sensor Electr. and Microsyst. Techn., 2015, 12(4), 27.
[36] Prepelitsa G. P., Buyadzhi V. V., Ternovsky V. B.: Photoelectronics., 2013, 22,103.
[37] Glushkov A. V., Khetselius O. Yu., Bunyakova Yu. Ya., Buyadzhi V. V., Brusentseva S. V., Zaichko P. A.: Sensor Electr. and Microsyst. Techn., 2014, 11(3), 62.
[38] Glushkov A. V., Ternovsky V. B., Buyadzhi V. V., Prepelitsa G. P. : Proc. Int. Geom. Centre., 2014, 7(4), 60.
[39] Glushkov A. V.,Kuzakon V. M., Khetselius O. Yu. Ternovsky: Proc. Int. Geom. Centre., 2015, 8(3-4), 69.
[40] Glushkov A V 2012 J. Phys.: Conf. Ser. 397, 012011
[41] Glushkov A. V., Khetselius O. Y. and Svinarenko A. A.: Phys. Scripta., 2013, T153, 014029.
[42] Svinarenko A. A.: J. Phys.: Conf. Ser. 2014, 548, 012039
[43] Glushkov A. V., Ambrosov S. V., Loboda A. V., Gurnitskaya E. P., Prepelitsa G. P.: Int. Journal Quant. Chemistry., 2005, 104, 562.
[44] Glushkov A. V., Efimov V. A., Gopchenko E. D., Dan’kov S. V., Polishchyuk V. N. and Goloshchak O. P.: Optics and Spectroscopy., 1998, 84, 670.
[45] Glushkov A. V., Lovett L., Khetselius O. Yu., Gurnitskaya E. P., Dubrovskaya Yu. V. and Loboda A. V.: Int. J. Modern Phys. A., 2009, 24, 611.
[46] Rusov V. D., Glushkov A. V., Vaschenko V. N. et al: Journ. of Atm. and Solar-Terrestrial Phys., 2010, 72, 498.
[47] Prepelitsa G. P., Glushkov A. V., Lepikh Ya. I., Buyadzhi V. V., Ternovsky V. B., Zaichko P. A.: Sensor Electr. and Microsystems Techn., 2014, 11, Issue 4, 43.
[48] Glushkov A. V., Prepelitsa G. P., Svinarenko A. A.: Proc. of Internat. Geometry Center, 2013, 6, Nо. 1, 67.
[49] Khetselius O. Yu., Glushkov A. V., Gurnitskaya E. P. etal: Spectral Line Shapes, Vol. 15-19th Internat. Conf. on Spectral Line Shapes (AIP), 2008, 15, 231.
[50] Khetselius O. Yu.: Spectral Line Shapes, Volume 15–19th Internat. Conf. on Spectral Line Shapes (AIP), 2008, 15, 363.
[51] Glushkov A. V., Khetselius O. Yu., Loboda A. V., Svinarenko A. A.: Frontiers in Quantum Systems in Chemistry and Physics (Springer), 2008, 18, 543.
[52] Glushkov A. V., Khetselius O. Yu., Lovett L.: Advances in the Theory of Atomic and Molecular Systems (Springer), 2009, 20, 125.
[53] Glushkov A. V., Ivanov L. N.: Phys. Lett. A.,1992,170, 33 [54] Ivanova E. P., Ivanov L. N., Glushkov A. V., Kramida A. E.: Phys. Scripta., 1985, 32, 513.
[55] Glushkov A. V., Ivanov L. N.: J. Physics B: Atomic, Mol. and Opt. Phys., 1993, 26, L379.
[56] Glushkov A. V., Ivanov L. N., Ivanova E. P.: Autoionization phenomena in atoms., M., Moscow State Univ., 1986, 58–160.
[57] Ivanova E. P., Glushkov A. V.: J. Quantitative Spectroscopy and Radiative Transf., 1986, 36, 127.
[58] Glushkov A. V., MalinovskayaS. V., Chernyakova Y. G., Svinarenko A. A., Int. Journal Quant. Chem., 2004, 99, 889.
[59] Glushkov A. V.: JETP Lett., 1992, 55, 97. [60] Glushkov A. V.: AIP Conference Proceedings., 2005, 796 (1), 206.
[61] Buyadzhi V. V., Zaichko P. A., Gurskaya M. Y., Kuznetsova A. A., Ponomarenko E. L., Ternovsky V. B.: J. Phys.: Conf. Series., 2017, 810, 012047
[62] Glushkov A. V., Kondratenko P. A., Buyadgi V. V., Kvasikova A. S., Sakun T. N., Shakhman A. N.: J. Phys.: Conf. Series., 2014, 548, 012025.
[63] Svinarenko A. A., Glushkov A. V., Khetselius O. Yu., Ternovsky V. B., Dubrovskaya Yu. V., Kuznetsova A. A., Buyadzhi V. V.: Theoretical Spectroscopy of Rare-Earth Elements: Spectra and Autoionization Resonances, In: Rare Earth Element. InTech, 2017, pp. 83–104 (DOI: 10. 5772/intechopen. 69314).
[64] Glushkov A. V., Khetselius O. Yu., Svinarenko A. A., Buyadzhi V. V., Ternovsky V. B., Kuznetsova A. A., Bashkarev P. G.: Relativistic Perturbation Theory Formalism to Computing Spectra and Radiation Characteristics: Application to Heavy Element, In: Recent Studies in Perturbation Theory. InTech, 2017, pp. 131–150 (DOI: 10. 5772/intechopen. 69102).
[65] Glushkov A. V., Khetselius O., Gurnitskaya E., Loboda A., Sukharev D.: AIP Conf. Proc., 2009, 1102, 168.
[66] Khetselius O. Yu.: Photoelectronics, 2005, 14, 83.
[67] Khetselius O. Yu.: Hyperfine structure of atomic spectra., Odessa, Astroprint, 2008.
[68] Khetselius O. Yu.: Sensor Electronics and Microsystem Techn., 2008, 3, 28.
[69] Khetselius O. Yu.: J. Phys.: Conf. Series., 2012, 397, 012012.
[70] Khetselius O. Yu., Florko T. A., Svinarenko A. A., Tkach T. B.: Phys. Scripta (IOP), 2013, T153, 014037.
[71] Khetselius O. Yu.: Int. J. Quant. Chem. 2009, 109, 3330
[72] Khetselius O. Yu.: Phys. Scr., 2009, T135, 014023
[73] Khetselius O. Yu.: AIP Conf. Proc., 2008, 1058, 363.
[74] Glushkov A. V., Rusov V. D., Ambrosov S., Loboda A.: New projects and new lines of research in nuclear physics, Eds. G. Fazio, F. Hanappe (World Scientific), 2003, 126
[75] Glushkov A. V., Malinovskaya S. V.: New projects and new lines of research in nuclear physics. Eds. G. Fazio and F. Hanappe (World Scientific), 2003, 242.
[76] Glushkov A. V.: Atom in electromagnetic field., Kiev, KNT, 2005.
[77] Glushkov A. V.: Relativistic and correlation effects in spectra of atomic systems., Odessa, Astroprint, 2006.
[78] Glushkov A. V., Safranov T. A., Khetselius O. Yu., Prepelitsa G. P., Mansarliysky V. F., Bykowszczenko N.: Environmental Problems. 2016, 1(2), 105.
[79] Glushkov A. V., Malinovskaya S. V., Gurnitskaya E. P., Khetselius O. Yu.,Dubrovskaya Yu. V.: J. Phys.: Conf. Series., 2006, 35, 425.
[80] Malinovskaya S. V., Glushkov A. V., Khetselius O. Yu., Lopatkin Yu. M., Loboda A. V., Svinarenko A. A., Nikola L. V., Perelygina T. B.: Int. Journ. Quant. Chem., 2011, 111, 288.
[81] Glushkov A. V., Ambrosov S. V., Ignatenko A. V., Korchevsky D. A.: Int. Journ. Quant. Chem., 2004, 99, 936.
[82] Malinovskaya S. V., Glushkov A. V., Khetselius O. Yu., Svinarenko A. A., Mischenko E. V., Florko T. A.: Int. Journ. Quant. Chem., 2009, 109, 3325.
[83] Glushkov A. V., Khetselius O. Yu., Malinovskaya S. V.: European Phys. Journal Special Topics, 2008, 160, 195.
[84] Glushkov A. V., Khetselius O. Yu., Malinovskaya S. V.: Molec. Phys. , 2008, 106, 1257.
[85] Glushkov A. V., Khetselius O. Yu., Svinarenko A. A., Prepelitsa G. P.: Energy Approach to Atoms in a Laser Field and Quantum Dynamics with Laser Pulses of Different Shape. In: Coherence and Ultrashort Pulse Laser Emission, Ed. by F. J. Duarte (InTech), 2010, 159.
[86] Malinovskaya S. V., Glushkov A. V., Dubrovskaya Yu. V., Vitavetskaya L. A.: Recent Advances in the Theory of Chemical and Physical Systems (Springer), 2006, 15, 301.
[87] Glushkov A. V., Khetselius O. Yu., Svinarenko A. A.: Advances in the Theory of Quantum Systems in Chem. and Phys., Ser.: Progress in Theor. Chem. and Phys., ed. by P. Hoggan, E. Brandas,J. Maruani, G. Delgado-Barrio, P. Piecuch (Springer), 2012, 22, 51
[88] Glushkov A. V., Malinovskaya S. V., Sukharev D. E., Khetselius O. Yu., Loboda A. V., Lovett L.: Int. Journ. Quantum Chem., 2009, 109, 1717.
[89] Glushkov A. V., Mansarliysky V. F., Khetselius O. Yu., Ignatenko A. V., Smirnov A. and Prepelitsa G. P.: J. Phys.: Conf. Ser., 2017, 810, 012034.
[90] Bunyakova Yu. Ya., Glushkov A. V., Khetselius O. Yu., Ignatenko A. V., Bykowszczenko N., Buyadzhi V. V.: Sensor Electr. And Microsyst. Techn., 2017, 14(3), 65.
[91] Glushkov A. V., Gurskaya M. Yu., Ignatenko A. V., Smirnov A. V., Serga I. N., Svinarenko A. A., Ternovsky E. V.: J. Phys.: Conf. Ser., 2017, 905, 012004.
[92] Khetselius O. Yu., Glushkov A. V., Gurskaya M. Yu., Kuznetsova A. A., Dubrovskaya Yu. V., Serga I. N., Vitavetskaya L.: J. Phys.: Conf. Ser., 2017, 905, 012029.
[93] Glushkov A. V., Malinovskaya S. V., Svinarenko A. A., Vitavetskaya L. A.: Sensor Electronics and Microsyst. Techn., 2005, 2(2), 29.
[94] Chernyakova Yu. G., Ignatenko V., Vitavetskaya L. A.: Sensor Electr. and Microsyst. Techn., 2004, 1(2), 20.
[95] Bystryantseva A. N., Khetselius O. Yu., Dubrovskaya Yu. V., Vitavetskaya L. A., Berestenko A. G.: Photoelectronics, 2016, 25, 56.
[96] Khetselius O. Yu., Lopatkin Yu. M., Dubrovskaya Yu. V., Svinarenko A. A.: Sensor Electr. and Microsyst. Techn., 2010, 2, 11.
[97] Glushkov A. V., Ambrosov S. V., Loboda A. V., Gurnitskaya E. P., Khetselius O. Y.: Recent Advances in Theor. Phys. and Chem. Systems., 2006, 15, 285.
[98] Glushkov A. V., Khetselius O. Yu., Loboda A. V., Svinarenko A. A.: Frontiers in Quantum Systems in Chemistry and Physics (Springer), 2008, 18, 525.